On quasiconformal non-equivalence of gasket Julia sets and limit sets

Abstract

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

arXiv comment25 pages without references, 7 figures. v2: minor changes

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